How to write a number in scientific notation
Example: in 0.000456, move the point 4 places right to get 4.56, so it's 4.56 × 10⁻⁴. In 6,020,000, move it 6 places left to get 6.02 × 10⁶.
Multiplying: multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10⁻²) = 6 × 10². Dividing: divide the coefficients and subtract the exponents. Adding or subtracting: rewrite both with the same exponent first: 3 × 10⁴ + 2 × 10³ = 3 × 10⁴ + 0.2 × 10⁴ = 3.2 × 10⁴.
E notation and engineering notation
Calculators and spreadsheets write 4.56 × 10⁻⁴ as 4.56e−4; the e means "times ten to the power of", not Euler's number. Engineering notation keeps the exponent a multiple of 3, so 4.56 × 10⁻⁴ becomes 456 × 10⁻⁶, which matches metric prefixes: 10³ is kilo, 10⁶ mega, 10⁻³ milli and 10⁻⁶ micro.
Significant figures are the digits that carry meaning. Rounding 6.0221 × 10²³ to 3 significant figures gives 6.02 × 10²³. Trailing zeros in a whole number like 1,200 are ambiguous; scientific notation makes them clear: 1.2 × 10³ has two significant figures and 1.200 × 10³ has four.
Frequently asked questions
How do you convert scientific notation to a decimal?
Move the decimal point right by the exponent if it's positive, or left if it's negative, adding zeros as needed. 3.5 × 10⁻⁴ = 0.00035.
What does 1e6 mean?
1 × 10⁶, which is 1,000,000. The number after e is the power of ten.
Can the coefficient be 10 or more?
Not in proper scientific notation. 12.3 × 10⁴ should be written 1.23 × 10⁵. Engineering notation does allow 1 to 999.
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